The computations performed in the pure gravity sector in this paper and the preceding ones [1]}, [2]}, [3]}, [4]}, demonstrating that amplitudes in compactified extra dimensional theories grow no faster than \(\mathcal {O}(s)\) , have important phenomenological consequences. The underlying higher-dimensional diffeomorphism invariance that ensures that scattering amplitudes are well behaved also guarantees that scattering amplitudes involving matter particles should also be compliant with the same principle. For example, in calculations for cosmological observables like relic abundances of dark matter with KK graviton portals (both for freeze-in and freeze-out), the velocity averaged cross sections must be properly estimated at large \(\sqrt{s}\) . An erroneous estimate with anomalously growing cross sections would lead to inaccurate predictions for cosmological observables within the scope of these models. We will illustrate these issues in detail in future work.
